Abstract. We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an rth order generalization of these operators and observe its approximation properties. Furthermore, we study ...

In this paper, we characterize the symbol in Hörmander symbol class S m ρ,δ (m ∈ R, ρ, δ ≥ 0) by its wavelet coefficients. Consequently, we analyse the kernel-distribution property for the symbol in the symbol class S m ρ,δ (m ∈ R, ρ > 0, δ ≥ 0) which is more general than known results; for non-regular symbol operators, we establish sharp L 2-continuity which is better than Calderón and Vaillan...

Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X → Y , which satisfies the inequality ||∆xf(y)− n!f(x)|| ≤ φ(x, y) for suitable control function φ, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of t 7→ f(tx) and t 7→ φ(tx, ty) imply the continuity of t 7→ M(tx).

Abstract. This paper proposes a novel technique to reduce noise whilst preserving edge sharpness during image filtering. This method is based on the image multi-resolution decomposition by a discrete wavelet transform, given a proper wavelet basis. In the transform space, edges are implicitly located and preserved, at the same time that image noise is filtered out. At each resolution level, geo...